The incident took place at Mankhurd around 7 am, when the youth, identified as Salman Khan, was learning to drive with the help of another person.
Khan has been arrested, police said.
"Khan lost control of the vehicle on the service road of Ghatkopar-Mankhurd Link Road. The car hit three school going children," DCP Shahaji Umap (Zone 6) said.
Anshika Yadav (7), Mahima Yadav (9) and Ganesh Yadav (12), who study in a nearby school, were injured in the accident, the official said.
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Mankhurd police registered a case under IPC sections 279 (rash driving), 337 (causing hurt by act endangering life or personal safety of others), 338 (causing grievous hurt by act endangering life or personal safety of others) along with the section 184 of Motor Vehicle Act, 1988.
"Salman's trainer has also been booked in this connection, although he is at large," Umap said.
Further investigation is on.